Towards the next generation of machine learning models in additive manufacturing: A review of process dependent material evolution

To improve the accuracy of these ML-driven regression models, the number of input parameters is significant. The more relevant input parameters are entered into the model, the more accurate the model would be. However, covering more input parameters requires a larger dataset, which is hardly obtainable in the AM field. Selecting the most significant input parameters is one way to reduce the data size required for developing an ML-driven regression model, which was employed by Ye et al. [208]. They implemented Spearman’s rank correlation [209] to select the most significant input parameters, consisting of the processing parameters (static) with the features extracted from the in-situ melt pool images to develop a semi-dynamic ML model with a small data size to predict the melt pool depth and height as summarized in Fig. 16.

Accessing a large dataset is a key parameter in accurately predicting the response in ML. In a study by Akbari et al. [101] a quite large experimental dataset has been collected from over 80 AM articles, including several processing conditions, material properties, melt pool dimensions, and flaw types. This benchmark was then used to develop several ML-driven regression and ML-driven classification models to predict the melt pool dimensions and flaw type, respectively, as indicated in Fig. 17. They also compared the performance of these models and the sensitivity of the models to the data size. Using the random forest, logistic regression, and neural network models, they visualized the decision boundaries for the dataset obtained from printing parts using Ti-6Al-4 V powder at different power and velocity values. They also used the confusion matrix to visualize the performance of the random forest model for different baseline plus absorptivity coefficients in Fig. 18. Although this large dataset could help cover several input parameters, many other input parameters are still missing, and also a limited range could be covered for each parameter compared to the big picture of AM. Generating a large dataset is not the only issue for developing an ML model, labeling this large dataset is also time-consuming and laborious. To obviate the labeling problem, in-situ data could be labeled using the ex-situ data in some cases, and then in-situ data could be employed to train a supervised machine learning model that can predict the final properties of the 3D-printed part on-the-fly. This approach was tested by Yuan et al. [210] to label in-situ video clips using the ex-situ height map analysis algorithm. The labeled in-situ data were then used to train a CNN model employed to predict the melt pool width, standard deviation, and track continuity.

To make the ML-driven regression models physics-informed, domain-specific knowledge and/or domain-specific constraints are required. Employing physics-based models that are iterative in nature (e.g., finite element methods) could be one alternative combined with data-driven ML models to generate PIML models. Employing a finite element model validated by experimental data to predict the temperature field and produce the data required to train an ML model is an example of a physics-informed ML-driven regression model employed by Pham et al.[212] and Fetni et al. [213] for a two-dimensional simulation and Roy et al. [214] for a three-dimensional fused filament fabrication (FFF) simulation indicated in Fig. 19. These models proposed a set of distance-based features by considering the characteristics of the thermal processes and built a PIMI model, which requires a smaller data size or is capable of covering a larger domain compared with previously proposed conventional ML models [64], [58], [215] based on temporal information that is critical in making the model PIMI-driven, as this information cannot be captured from in-situ temperature data alone. It is worth mentioning that laws of physics are employed in the PIML models to cover the missing information, which cannot be captured using experiments, and experiments are employed along with laws of physics to justify and cover the assumptions that simplify the physics-informed models (e.g., constant thermophysical properties, sophisticated effects of microstructure, etc.). An ML model cannot be called physics-informed in the absence of one of these main components. For instance, the proposed data-driven methods by Mozaffar et al. [64] and Ren et al. [216] were not demonstrated on real-time experimental data and were hardly convinceable to consider them as physics-informed ML models, as laws of physics should be an assistive tool, constraining the domain under study. This point was clearly indicated in a study by Ren and Wang [217] by developing Gaussian process regression models to predict the melt pool volume using a simulated dataset, an experimental dataset, and a mix of the simulated and experimental datasets. They indicated that the melt pool volume suddenly had a large overshoot due to heat accumulation as depicted in Fig. 20. This large melt pool overshoot was controlled by significantly reducing the laser power of the second and the subsequent tracks. Then, the physics-informed Gaussian process regression model was used to predict this dynamic evolution of the melt pool, as depicted in Fig. 20. It was also found that the model performance can be improved by mixing the numerical and experimental datasets when the experimental data size is not large enough, as the high-fidelity simulated dataset, even though subject to errors, at least can catch the trend of the real-time experimental data. This helps achieve a PIML model with a limited number of experimental data, which could be employed to accurately predict the melt pool size.

To reduce the dependency on a large number of datasets, Zhu et al. [218] introduced a PIMT model, a physics-informed neural network (PINN) model, that incorporates both data and fundamental principles of physics (i.e., continuity, momentum, and energy governing equations) into a deep neural network to inform the training processes. To do this, the loss function used in conventional deep neural networks to measure the model performance against ground truth values was modified by these laws of physics, which were often expressed as a set of PDEs with appropriate initial and boundary conditions, and was penalized by the residuals of the Navier–Stokes and energy conservation equations on a set of collocation points. They demonstrated that their PINN model is capable of predicting temperature and melt pool dynamics using a moderate number of labeled datasets, as depicted in Fig. 21. However, the model developed in their study was oversimplified and did not reflect the complexity of metal AM processes, as free-surface deformation of the melt pool, evaporation phenomenon, and ambient gas phase were not considered in the developed PIMT model. Employing multi-phase Navier–Stokes equations modified by missing phenomena (e.g., evaporation) to capture the heat loss, liquid fraction change, and fluid motion and applying additional PDEs (e.g., convection equation of level set and volume of fluid approach) used in the previous studies [219], [220] could be a great continuation of Zhu et al. study [218].

Selecting the scanning strategy based on the previous thermal history may not be practical from in-situ data alone. However, physics-informed models could assist to make it possible. Ren et al. [221] developed a PIMI model using an FE model to map the temperature field and scanning pattern traced for material deposition for every unit of the simulation step, as depicted in Fig. 22. Extracting this time-sensitive deposition information was critical in making a PIMI model, as this model is not easily achievable from in-situ temperature data alone. In another study [162], the same authors employed an RNN approach for developing a PIMI model to predict the thermal distribution of the next layer using the thermal field of two previous deposited layers and the candidate scan strategy. The temperature distribution predicted using the PIMI model is further employed to select the most suitable scan strategy for the next layer, which minimizes the local heat accumulation during the deposition. The process continues until the fabrication is complete.

ML classification approaches have been mainly used to detect defects and anomalies in the AM field. Mahmoudi et al. [222] developed a system to detect printing process deviations by capturing the in-situ thermal field of melt pools during fabrication. As depicted in Fig. 23, a similar approach was taken in a study by Seifi et al. [223] to detect the thermal-defect relationship in real-time manufacturing, as there is a direct relationship between the thermal history of the 3D-printed part and its microstructure. To identify this relationship, the highly dynamic thermophysical AM process captured by a pyrometer camera during manufacturing was characterized by developing a tensor-based modeling approach. The key layerwise signature features were extracted from the melt pool images by multilinear principal component analysis (MPCA) and these features were employed to predict the overall quality of the deposited layers using an SVM classifier.

Acoustic emission was also used as the input of an LR model to detect two types of primary defects (i.e., crack and porosity) in a study by Gaja et al. [224]. The results showed the high potential capability of acoustic emission for assessing the overall deposition quality and identifying defects, as indicated in Fig. 24. Although the models developed in Gaja et al. study [224] revealed a promising accuracy in detecting defects, their model should be further extended to cover other types of defects, such as balling, lack-of-fusion, etc. To do this, the LR model employed by Gaja et al. [224] may not be capable to be used in non-binary classification tasks with more than two labels. Thus, this model is not suggested for classification problems. CNN model could be a proper alternative employed in a study by Shevchik et al. [225] to classify the quality of 3D-printed parts into poor, medium, and high through linking acoustic emission of the parts printed at different processing parameters to their qualities. They also used spectral convolutional neural networks (SCNN) [189], [226], a recent extension of CNN, to develop a model and compared the accuracy of their CNNs and SCNNs models together. These efforts were also further extended by Ye et al. [227] to link acoustic emission to five different melt states (i.e., underheating, medium underheating, normal, medium overheating, and overheating) formed at different processing parameters using an SVM model. The results showed a fairly high accuracy if all the acoustic emission features are used, and no PCA or FDA dimensionality reduction is conducted for data dimensionality reduction, as these dimensionality reduction methods worked more like a feature extraction method rather than real feature selection in their study.

Linking the morphology of the 3D-printed parts to the defect formation is another way to evaluate the overall quality of deposited layers. Gobert et al. [228] used SVM to detect defects on a staircase cylinder by labeling different defects (i.e., porosity, incomplete fusion, crack, or inclusion). To develop such a model, multiple images were collected at each printed layer and multi-dimensional visual features were extracted and evaluated using a binary classification technique. The regions were then categorized as either a defect or a nominal build condition. The true location of the defects and nominal build areas were then obtained using a CT scan [47], which was then transferred into a layerwise image domain and fed into the classifiers. These steps are indicated in a flowchart in Fig. 25. Khanzadeh et al. [16] developed an ML framework to establish a relationship between the melt pool morphological characteristics and defects in the microstructure, as indicated in Fig. 26. They employed thermal images to find the melt pool profile and functional principal component analysis to extract the critical features of the melt pools, which are responsible for the majority of the variations in the melt pool. They then used this information to train different ML models (i.e., KNN, SVM, DT, DA), predict defects in the AM parts, and compare the accuracy of these models using the highest rate of accurately classifying melt pools ($M_1$) and lowest rate for incorrectly identifying normal melt pools as pores ($M_2$) as listed in Table 2. Similarly, the type and severity of porosity have been linked to physically intuitive process signatures (i.e., melt pool length, temperature gradient, and ejecta or spatter characteristics), which were extracted from melt pool images, using relatively simple ML models (KNN, LR, and SVM) in a study by Smoqi et al. [229]. The accuracy of these models was then compared with a more complex ML model (i.e., CNN), which directly used raw melt pool images. This procedure was indicated in Fig. 27. The results indicated that the relatively simple ML models trained with pragmatic physically informed melt pool shapes are as effective for defect prediction as using a complex CNN model. In another study [230], a dense convolution network (DenseNet) model was selected among four different models (i.e., AlexNet, GoogLeNet, ResNet, DenseNet) due to better distinguishing information than other models to predict the relationship between the melt pool shape and melt pool states (i.e., normal melting, incomplete melting, and discontinuity melting states) as depicted in Fig. 28. CNN was also employed to classify the melt pool size, which helps detect irregular melt pool formation, without considering spattering using in-situ melt pool monitoring in a study by Yang et al.[231] and detected defects in 3D-printed parts by processing the geometrical anomalies in a study by Khan et al. [232]. The model developed in the latter study integrated the concepts of image processing-computer vision and machine learning and evaluated the effect of various parameters (i.e., input size, batch size, validation split, class mode, activation function, optimizer, steps per epoch, number of epochs), affecting the accuracy of the model as depicted in Fig. 29. Similar to all other conventional data-driven methods, their model requires a large dataset and can be further optimized by enabling defect detection in the vertical plane and by classifying the cause of the defects. In detection and classification problems, CNN is the most common approach widely used in the AM field [233].

The ML models developed earlier for classification problems are well known for their exemplary performance to learn complex process-property correlations. However, these models are limited to machine settings and ignore the physical laws of the problem. If the machine, components, or range of processing parameters change, the dominant laws of physics may change due to these changes, and consequently, these models fail. In classification problems, developing PIML models is an appropriate solution to obviate such a problem using ML models, which are employed more often in recent publications. In a study by Liu et al. [237], porosity sizes categorized into three levels (i.e., pass, flag, and fail) were correlated with the laser-related physical effects instead of machine setting parameters using six different ML models. The accuracy of the PIML model developed in their study was compared with the accuracy of an ML model that directly used machine setting parameters. They concluded that the ML model developed using the machine setting parameters has nearly the same performance as the PIML model, as depicted in Fig. 30. However, the PIML model does not rely on the machine setting and can be applied to predict quality in different machines and settings.

Mechanistic input parameters predicting balling defect [238], [239] using 6 out of 10 most important processing parameters and material properties is a good example of the PIMI model employed by Du et al. [240] summarized in Fig. 31. Also, the thermal history of an AM part was predicted from the datasets containing generic and engineered features constructed based on the physics of the underlying thermal process using an extremely randomized tree model in a study conducted by Ness et al. [241]. In their work, the domain knowledge provided the laws of physics and made the model PIMI that corrects, enriches, and enhances the data. They demonstrated that simulation-to-simulation predictions are possible with high accuracy for the transferability of thermal histories between a variety of patterns, geometries, meshes, and power intensities, which proves the potential of PIMI in AM. A summary of the supervised models reviewed here is listed in Table 3.

Another significant research thrust in AM is to develop online ML methods for in-situ monitoring of the AM processes and link these data to a feedback control system that adjusts experimental parameters on the fly. Developing models capturing the complexity of AM processes is now achievable through the use of high-performance computers. However, taking these data into the production environment is still a challenge, which can be achieved by leveraging both numerical and experimental data from a structured database. Developing online PIML models by a combination of numerical and experimental data suggested by Yan et al. [220] may be a great solution to online monitoring of the AM processes and modifying them based on the live feedback collected during the process, as indicated in Fig. 32. Towards developing such a framework, online ML models have been developed to rapidly detect surface defects by developing an in-situ point cloud processing that enables live surface monitoring with no need for sensor intermittence [246]. However, involving more physical phenomena in the problem by including micro-scale models (e.g., electron or photon material interactions causing heat generation), mesoscale models (e.g., individual power particle evolution driven by fluid flow and thermal diffusion, surface tension force, Marangoni effect), and macro-scale models (e.g., FEA codes to resolve the fabrication process of a complex product) could further improve the performance of the model toward developing online PIML models.